Question

A car covers a distance of 260 km at a constant speed. It would have taken 1h 5 minutes less to travel
the same distance, if its speed was 20 kmph more. Find the speed of the car. (in kmph)
(1) 60
(2) 80
(3) 75
(4) 70
plz answer it quickly​

Answer 1

Answer:

(2) 80

Step-by-step explanation:

Define x :

Let the speed be x km/h

Find the time taken in term of x:

Distance = 260 km

Time taken = Distance ÷ Speed

Time taken 260/x

Find the time taken if the speed is 20 km/h more:

Distance = 260 km

Time taken = Distance ÷ Speed

Time taken 260/(x + 20)

The time taken is 1 hour 5 mins longer

1 hour 5 mins = 65/60 hour = 13/12 hour

Solve x :

260/x - 260/(x + 20)  = 13/12

[ 260(x + 20) - 260x ] / x(x + 20) = 13/12

[ 260x + 5200 - 260x ] / x(x + 20) = 13/12

5200/ x(x + 20) = 13/12

12 x 5200 = 13x(x + 20)

62400 = 13x² + 260x

13x² + 260x - 62400 = 0

x² + 20x - 4800 = 0

(x - 80)  (x + 60) = 0

x = 80 or x = - 60 (rejected)

Answer: (2) 80